2.The face value of the treasury security is $1,000.If this security earns 5%, then in one year
we will receive $1,050.Thus:

NPV = C0 + [C1/(1 + r)]
= -1000 + (1050/1.05) = 0

This
is not a surprising result, because 5 percent is the opportunity cost of
capital, i.e., 5 percent is the return available in the capital market.If any investment earns a rate of return
equal to the opportunity cost of capital, the NPV of that investment is zero.

3.NPV =
-$1,300,000 + ($1,500,000/1.10) = +$63,636

Since the NPV is positive, you would
construct the motel.

Alternatively, we can compute r as
follows:

r =
($1,500,000/$1,300,000) – 1 = 0.1538 = 15.38%

Since the rate of return is greater than the cost
of capital, you would construct the motel.

4.

Investment

NPV

Return

1)

2)

3)

4)

a.Investment 1, because it has the highest NPV.

b.Investment 1, because it maximizes shareholders’ wealth.

5.a.NPV =
(-50,000 + 30,000) + (30,000/1.07) = $8,037.38

b.NPV =
(-50,000 + 30,000) + (30,000/1.10) = $7,272.73

Since,
in each case, the NPV is higher than the NPV of the office building ($7,143),
accept E. Coli’s offer. You can also think of it another way.The true opportunity cost of the land is
what you could sell it for, i.e., $58,037 (or $57,273).At that price, the office building has a
negative NPV.

6. The
opportunity cost of capital is the return earned by investing in the best
alternative investment.This return
will not be realized if the investment under consideration is undertaken.Thus, the two investments must earn at least the same return.This return rate is the discount rate used
in the net present value calculation.

7.a.NPV =
-$2,000,000 + [$2,000,000 ´
1.05)]/(1.05) = $0

b.NPV =
-$900,000 + [$900,000 ´
1.07]/(1.10) = -$24,545.45

The correct discount rate is 10%
because this is the appropriate rate for an investment with the level of risk
inherent in Norman’s nephew’s restaurant.The NPV is negative because Norman will not earn enough to compensate
for the risk.

c.NPV
= -$2,000,000 + [$2,000,000 ´
1.12]/(1.12) = $0

d.NPV = -$1,000,000 + ($1,100,000/1.12) = -$17,857.14

Norman should invest in either the risk-free government
securities or the risky stock market, depending on his tolerance for risk.Correctly priced securities always have an
NPV = 0.

8.a.Expected rate of return on project =

This
is equal to the return on the government securities.

b.Expected rate of return on project =

This
is less than the correct 10% rate of return for restaurants with similar risk.

c.Expected
rate of return on project =

This is equal to the
rate of return in the stock market.

d.Expected rate of return on project =

This is less than the return in the equally risky stock market.

9.

The rate at which Norman can borrow
does not reflect the opportunity cost of the investments.Norman is still investing $1,000,000 at 10%
while the opportunity cost of capital is 12%.

10.a.This is incorrect.The cost of capital is an opportunity cost;
it is the rate of return foregone on the next best alternative investment of
equal risk.

b.Net present value is not “just theory.”An asset’s net present value is the net gain
to investors who acquire the asset.The
concept of “maximizing profits” is the fuzzy concept here.For example, this goal does not make it
clear whether it is appropriate to try to increase profits today if it means
sacrificing profits tomorrow.In contrast
to the objective of maximizing profits, the net present value criterion correctly
accounts for the timing of returns from an investment.

Note that “maximize profits” is an unsatisfactory objective in
other respects as well.It does not
take risk in to account, so that it is not possible to determine whether it is worth
trying to increase (average) profits if, in the process, risk is also
increased.It is also unclear which
accounting figure should be maximized because the profit figure depends on the
accounting methods chosen.It is cash
flow that is important, not accounting profit.Cash flow can be spent or invested, while accounting profit is a number
on a piece of paper which can change with changes in accounting methods.

c.The comment can be interpreted in two ways:

1.The manager may try to boost stock price temporarily by
disseminating a deceptively rosy picture of the firm’s prospects.This possibility is not considered in this
chapter.However, it is difficult to
imagine how a manager can act in the stockholders’ best interests by deceiving
them.

2.The manager may sacrifice present value in order to achieve
the “gently rising trend.”This is not
in the stockholders’ best interests.If
they want a gently rising trend of wealth or income, they can always achieve it
by shifting wealth through time (i.e., by borrowing or lending).The firm helps its stockholders most by
making them as rich as possible now.

11.The investment’s positive NPV will be
reflected in the price of Airbus common stock.In order to derive a cash flow from her investment that will allow her
to spend more today, Ms. Smith can sell some of her shares at the higher price
or she can borrow against the increased value of her holdings.

12.

a.Let x = the amount that Casper should invest now.Then ($200,000 – x) is the amount he will
consume now, and (1.08 x) is the amount he will consume next year.

Since
Casper wants to consume exactly the same amount each period:

200,000 – x =
1.08 x

Solving, we find that x = $96,153.85
so that Casper should invest $96,153.85 now, he should spend ($200,000 -
$96,153.85) = $103,846.15 now and he should spend (1.08 ´ $96,153.85) = $103,846.15 next
year.

b.Since Casper can invest $200,000 at 10% risk-free, he can
consume as much as ($200,000 ´
1.10) = $220,000 next year.The present
value of this $220,000 is: ($220,000/1.08) = $203,703.70, so that Casper can
consume as much as $203,703.70 now by first investing $200,000 at 10% and then
borrowing, at the 8% rate, against the $220,000 available next year.If we use the $203,703.70 as the available
consumption now, and again let x = the amount that Casper should invest now, we
can then solve the following for x:

$203,703.70
– x = 1.08 x

x =
$97,934.47

Therefore, Casper should invest $97,934.47 now at 8%, he should
spend ($203,703.70 – $97,934.47) = $105,769.23 now, and he should spend
($97,934.47 ´
1.08) = $105,769.23 next year.[Note
that this approach leads to the result that Casper borrows $203,703.70 at 8%
and then invests $97,934.47 at 8%.We
could simply say that he should borrow ($203,703.70 - $97,934.47) = $105,769.23
at 8% against the $220,000 available next year.This is the amount that he will consume now.]

13. “Well functioning” means investors all
have free and equal access to competitive
capital markets.Maximizing value may
not be in all shareholders’ interest if different shareholders are taxed at
different rates, or if they do not or can not receive important information at
the same time (due to differences in costs or abilities), or if they have
different access to the capital markets.

14.If a firm does not have a reputation for honesty and fair business
practices, then customers, suppliers, and investors will not want to do
business with the firm.The firm, by
acting in such a fashion, will not be able to maximize the value of the firm
and shareholders will start to sell and the stock price will fall.The further the stock price falls, the
easier it is for another group of investors to buy control of the firm and to
replace the old management team with one that is more responsive to its
stockholders.

Challenge Questions

1.The two points raised in the question do not invalidate the
NPV rule.

a.As long as capital markets do their job, all members of the
community, wealthy or poor, have the same rate of time preference, because they
all adjust to the same borrowing-lending line.The government acts in the best interests of all of its citizens by
choosing only investments having positive NPV when discounted at the market
interest rate.

b.The “longer horizon” argument, to the extent it is valid,
requires a lower discount rate.It does
not require discarding the NPV concept.But should the government ever use a lower discount rate?Note that the rate of return on incremental
real investment in the private sector equals the market rate of interest.Why should the government divert resources
into public investments offering a lower rate of return?Lowering the discount rate for public
investment means allowing the government to invest resources at a lower rate of
return.That would not help future
generations.

There are some cases where a lower discount rate might be
justified, however.For example, NPV
analysis might indicate that a wilderness mountain meadow should be torn up in
order to create a copper mine, but We the People might decide to make it a
national park instead.In part, this
decision reflects the difficulty of capturing intangible benefits of the park
in an NPV calculation.Even if the
intangibles could be expressed as dollar values, there is a case for
discounting at a relatively low rate: People’s time preferences for wilderness
recreation may not fully adjust to capital market rates of return.

2.a.1 + r = 5/4 so that r = 0.25 = 25 percent

b.$2.6 million – $1.6 million = $1 million

c.$3 million

d.Return = (3 – 1)/1 = 2.0 = 200 percent

e.Marginal rate of return = rate of interest = 25 percent

f.PV = $4 million – $1.6 million = $2.4 million

g.NPV = -$1.0 million + $2.4 million = $1.4 million

h.$4 million ($2.6 million cash + NPV)

i.$1 million

j.$3.75 million

3.a-d.See
Figure 2.1a on separate web page

e.NPV = C0 + C1/(1
+ r)

$2 million = -$6 million
+ C1/(1 + 0.10)

C1 = $8.8
million

f.The marginal rate of return equals the interest rate, 10
percent.

g.After the firm has announced its investment plans, the firm’s
PV is equal to the amount of cash initially available ($10 million) plus the PV
of the investment ($2 million).Thus,
the firm’s PV after the announcement is $12 million.

h.After the company pays out $4 million, the shareholders have
$4 million in cash plus shares worth $8 million.(We know the shares are worth $8 million because the PV of
their total investment is $12 million.)In order to spend as they desire, they must borrow $2 million.The interest rate is 10 percent.

i.Next year, they will have the cash
flow at t = 1, which is $8.8 million, but they will also have to repay the loan
(plus interest, of course):

The net cash flow from selling the tanker load is the same
as the payoff from one million shares of Stock Z in each state of the world
economy.Therefore, the risk of each of
these cash flows is the same.

d.NPV = -$8,000,000 + ($12,000,000/1.20) = +$2,000,000

The project is a good investment because the NPV is
positive.Investors would be prepared to
pay as much as $10,000,000 for the project, which costs $8,000,000.